Problem: What is the amplitude of $g(x)=-9\cos\left(\dfrac{\pi}{2} x-6\right)+8$ ?
Explanation: Amplitude in sinusoids of the form $f(x)=a\cos(bx+c)+d$ The amplitude of a sinusoid of the form $f(x)={a}\cos(bx + c) + d$ is equal to $|{a}|$. [How can we justify this given our graphical understanding of amplitude?] Finding the amplitude The amplitude of $g(x) = {-9}\cos\left(\dfrac{\pi}{2} x-6\right)+8$ is $|{-9}|=9$.